Former Prime Minister Ehud Barak edged out political newcomer Ami Ayalon 36 percent to 31 percent, according to final results announced early Tuesday. But Barak fell short of the 40 percent threshold needed for an outright victory, setting the stage for a June 12 runoff against Ayalon.
About 65 percent of 104,000 eligible voters participated in the primary. The current Labor leader, Defense Minister Amir Peretz, finished third with 22 percent, while two other candidates lagged far behind with single-digit support.
Labor has served as the junior partner in Olmert's year-old government.
But either Barak or Ayalon are expected to shake up that alliance. Both have called for Olmert's resignation in the wake of a highly critical government report on his performance during last summer's war in Lebanon. It's unclear, however, how quickly they would work for his ouster.
Ayalon, a former navy chief and ex-head of the Shin Bet internal security agency, entered parliament only last year. He won support as a newcomer to the political scene, while also holding the security credentials demanded by Israeli voters.
Ayalon, 61, has pledged to lead the centrist Labor out of its year-old partnership with Olmert if the prime minister's Kadima Party doesn't choose a new leader.
"I think many people understand that we are, in fact, not just voting on the future of the Labor Party but to a very large extent on the future leadership of the state of Israel," he said at the northern Israel polling station where he cast his ballot.
Barak, meanwhile, tried to persuade voters that his experience made him the best man for the job. A former military chief and the country's most decorated soldier, the 65-year-old served as prime minister from 1999 to 2001.
Barak has said he would serve temporarily in an Olmert government, while also pushing for early elections. Olmert was elected last year to what is supposed to be a four-year term.
Both Ayalon and Barak could face a tough time leading their party out of the government. Many senior Labor officials favor staying in the government, wanting to hold on to power and fearful that the party could lose in a new vote.
Opinion polls forecast the hard-line Likud Party, led by former Prime Minister Benjamin Netanyahu, would win a new election.
Additional time could benefit Ayalon or Barak. As a political newcomer, Ayalon would like to build his popularity inside Labor and with the general public. Barak, unseated as premier following eruption of the Palestinian uprising seven years ago, would like a senior Cabinet post to rehabilitate his tarnished image.
Casting his ballot in the central city of Kfar Saba, he touted his defense credentials and raised the specter of a Netanyahu premiership.
"I tell voters only two things: I tell them to think about who they want more in a time of war, and I tell them that only with me heading our team can we beat Netanyahu," he said.
Israeli analyst Yossi Alpher said early elections appear inevitable. Both candidates could say, "'I won't bring down the government, but Olmert should be replaced,"' Alpher said. "One way or another, it means in about a year there will be early elections."
Should the 19-member Labor faction bolt the government, Olmert could try to avert elections by propping up his government with religious or hawkish parties opposed to making concessions to the Palestinians.
Alternatively, with Labor demanding that he step down, the embattled Olmert might face new pressure within Kadima to comply.
Tuesday's results ended Peretz's troubled stint as Labor leader. A fiery union leader of Moroccan descent, Peretz took the chairmanship less than two years ago in an upset victory that had many Israelis forecasting a new era for Israeli politics.
But when Olmert put together his coalition last year, political maneuvering kept Peretz out of the finance minister's post he coveted. Instead, he became defense minister, and his political star quickly sank following the inconclusive war against Hezbollah militants in Lebanon.
Peretz had said he would leave the defense job regardless of the vote. Based on his third-place finish, he could emerge as a kingmaker in the runoff, positioning him for a senior Cabinet post if Labor remains in the government.
Both Barak and Ayalon are expected to seek the defense minister position.